6(2a-1)=-2a(a+17)

Solution for 6(2a-1)=-2a(a+17) equation:

6(2a-1)=-2a(a+17)

We move all terms to the left:

6(2a-1)-(-2a(a+17))=0

We multiply parentheses

12a-(-2a(a+17))-6=0


We calculate terms in parentheses: -(-2a(a+17)), so:

-2a(a+17)

We multiply parentheses

-2a^2-34a

Back to the equation:

-(-2a^2-34a)


We get rid of parentheses

2a^2+34a+12a-6=0

We add all the numbers together, and all the variables

2a^2+46a-6=0

a = 2; b = 46; c = -6;
Δ = b2-4ac
Δ = 462-4·2·(-6)
Δ = 2164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{541}}{2*2}=\frac{-46-2\sqrt{541}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{541}}{2*2}=\frac{-46+2\sqrt{541}}{4}
$